Answer:
20 g/mol
Explanation:
We can use Graham’s Law of diffusion:
The rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M).
[tex]r = \frac{1 }{\sqrt{M}}[/tex]
If you have two gases, the ratio of their rates of diffusion is
[tex]\frac{r_{2}}{r_{1}} = \sqrt{\frac{M_{1}}{M_{2}}}[/tex]
Squaring both sides, we get
[tex](\frac{r_{2}}{r_{1}})^{2} = \frac{M_{1}}{M_{2}}[/tex]
Solve for M₂:
[tex]M_{2} = M_{1} \times (\frac{r_{1}}{r_{2}})^{2}[/tex]
[tex]M_{2} = \text{39.95 g/mol} \times (\frac{\text{3.2 cm/s}}{\text{4.5 cm/s}})^{2}= \text{39.95 g/mol} \times (0.711 )^{2}[/tex]
[tex]= \text{39.95 g/mol} \times 0.506 = \textbf{20 g/mol}[/tex]
